Question

A satellite orbits the Earth with an elliptical orbit modeled by $x$ squared over $47$ million three hundred thirty four thousand four hundred plus y squared over forty three million nine hundred fifty six thousand nine hundred equals $1$ comma where the distances are measured in km.

The Earth shares the same center as the orbit. If the radius of the Earth is $6370km$ , what is the maximum distance between the satellite and the Earth?

Answer 1

Maximum distance between the satellite and the Earth :

The equation on which satellite revolves = $\frac{x^2}{47334400}+\frac{y^2}{43956900}=1$

General equation of elliptical orbit = $\frac{x^2}{a^2}+\frac{y^2}{b^2}=1$

Comparing both equations, we get

$$\begin{gathered} \Rightarrow a^2=4733400 \\ \therefore a=6880km \end{gathered}$$

$$\begin{gathered} \Rightarrow b^2=43956900 \\ \therefore b=6630km \end{gathered}$$

The Earth is revolving around the same center with the radius $=6370km$

$\therefore$ Maximum distance between the satellite and the Earth $=6880-6370$

$=510km$